non-Euclidean geometry は、 n-sphere を扱うが、 n-sphere 自体がn-次元で二次元では無く、又、Euclid の fifth postulate
If the sum of the interior angles α and β is less than 180°, the two straight lines, produced indefinitely, meet on that side.
If a line segment intersects two straight lines forming two interior angles on the same side that are less than two right angles , then the two lines, if extended indefinitely, meet on that side on which the angles sum to less than two right angles.
を読み違えており、Euclidは、二次元の直線のことを言っているが、理解出来ず、三次元の曲線は無関係である。
ὅπερ ἔδει δεῖξαι
T.theodor
